Light
Properties of light are fundamental
Almost everything we know about the universe outside our solar system comes from interpreting the light from distant objects.
Light is weirder than you think
Here are some slides I’ve used for introductory astronomy as a guide to some properties of light.  The math here might be useful in figuring out your own stories involving light.

Radiation: Two different kinds
Something that “radiates”, or spreads out in “rays”
High speed particles (eg. high speed neutrons ejected from a disintegrating atomic nucleus)
Electromagnetic radiation:
Towards shorter “wavelength” and higher energy:
Visible light, Ultraviolet light, X-Rays, Gamma-Rays
Towards longer “wavelength” and lower energy:
Visible light, Infrared radiation, microwaves, radio waves

Properties of Light
Light has both wave and particle properties
Travels like a wave
Interacts with matter like a particle:  “photon”
Full explanation involves quantum mechanics
For most cases we can just choose the right “model” from the above two choices
Photons, unlike particles in other kinds of “radiation,” are particles of “pure energy”

Light is an electromagnetic wave
Changing electric fields generates magnetic fields
Changing magnetic fields generates electric fields
Can set up a cycle where one field causes the other:
The E and B fields oscillate in strength, and the disturbance moves forward.
To describe the wave you need to specify
Direction it is moving
Strength of the fields (its intensity)
Frequency or Wavelength of the oscillation (u and l are inversely related)
Orientation of the electric E field:  up or sideways (polarization)
You do not need to specify its speed
In a vacuum all lightwaves move at the same speed c = 3´108 m/s

The Electromagnetic Spectrum
Radio waves
Microwaves
Infrared
Visible
Ultra-violet
X-Rays
Gamma rays

Relationship between Energy and Wavelength of Light
Short wavelength Þ  High energy photons
Long  wavelength Þ Low energy  photons
Intensity µ total energy (per area per second)

              
µ          (# of photons per area per second)
                      
´  (energy per photon)
Example with falling rain:
Amount of rain µ (# of raindrops) ´ (volume per drop)

Why is energy per photon so important?
Real life example:  Ultra-Violet light hitting your skin
Threshold for chemical damage set by energy (wavelength) of photons
Below threshold (long wavelengths) energy too weak to cause chemical changes
Above threshold (short wavelength) energy  photons can break apart DNA molecules
Number of molecules damaged = number of photons above threshold
Very unlikely two photons can hit exactly together to cause damage

Numerical Relationship between
 wavelength and photon energy
Inverse relationship:  Smaller l means more energetic
c = speed of light = 3.00 ´ 108 m/s
h = Planck’s constant = 6.63 ´ 10-34 joule/s
Note:  Joule is a unit of energy        1 Joule/second = 1 Watt
Energy of a single photon of 0.5 mm visible light?
Seems very small, but this is roughly the energy it takes to chemically modify a single molecule.
Photons from a 100 W lightbulb  (assuming all 100W goes into light?)

Temperature and Heat
Thermal energy is “kinetic energy” of moving atoms and molecules
Hot material energy has more energy available which can be used for
Chemical reactions
Nuclear reactions (at very high temperature)
Escape of gasses from planetary atmospheres
Creation of light
Collision bumps electron up to higher energy orbit
It emits extra energy as light when it drops back down to lower energy orbit
(Reverse can happen in absorption of light)

Temperature Scales
Want temperature scale where energy is proportional to T
Celsius scale is “arbitrary”  (Fahrenheit even more so)
0o C     = freezing point of water
100o C = boiling point of water
By experiment, available energy = 0 at “Absolute Zero” = –273oC  (-459.7oF)
Define “Kelvin” scale with same step size as Celsius, but 0K = -273oC = Absolute Zero
Use Kelvin Scale for most of work in this course
Available energy is proportional to T, making equations simple (really! OK, simpler)
273K = freezing point of water
373K = boiling point of water
300K   approximately room temperature

Planck “Black Body Radiation”
Hot objects glow (emit light)
Heat (and collisions) in material causes electrons to jump to high energy orbits
As electrons drop back down, some of energy is emitted as light.
Reason for name “Black Body Radiation”
In a “solid” body the close packing of the atoms means than the electron orbits are complicated, and virtually all energy orbits are allowed.  So all wavelengths of light can be emitted or absorbed.  (In a gas with isolated atoms, only certain orbits are permitted so only certain wavelengths can be absorbed or emitted.)
A  black material is one which readily absorbs all wavelengths of light.  These turn out to be the same materials which also readily emit all wavelengths when hot.
The hotter the material the more energy it emits as light
As you heat up a filament or branding iron, it glows brighter and brighter
The hotter the material the more readily it emits high energy (blue) photons
As you heat up a filament or branding iron, it first glows dull red, then bright red, then orange, then if you continue, yellow, and eventually blue

Planck and other Formulae
Planck formula gives intensity of light at each wavelength
It is complicated.  We’ll use two simpler formulae which can be derived from it.
Wien’s law tells us what wavelength has maximum intensity
Stefan-Boltzmann law tells us total radiated energy per unit area

Example of Wien’s law
What is wavelength at which you glow?
Room T = 300 K so
This wavelength is about 20 times longer than what your eye can see.  Camera in class operated at 7-14 μm.
What is temperature of the sun – which has maximum intensity at roughly 0.5 mm?

Kirchoff’s laws
Hot solids emit continuous spectra
Hot gasses try to do this, but can only emit discrete wavelengths
Cold gasses try to absorb these same discrete wavelengths

Atoms – Electron Configuration
Molecules:  Multiple atoms sharing/exchanging electrons  (H2O, CH4)
Ions:          Single atoms where one or more electrons have escaped  (H+)
Binding energy:   Energy needed to let electron escape
Permitted “orbits” or energy levels
By rules of quantum mechanics, only certain “orbits” are allowed
Ground State:  Atom with electron in lowest energy orbit
Excited State:  Atom with at least one atom in a higher energy orbit
Transition:    As electron jumps from one energy level orbit to another,
  atom must release/absorb energy different, usually in form of light.
Because only certain orbits are allowed, only certain energy jumps are allowed, and atoms can absorb or emit only certain energies (wavelengths) of light.
In complicated molecules or “solids” many orbits and transitions are allowed
Can use energy levels  to “fingerprint” elements and estimate temperatures.

Hydrogen Lines
Energy absorbed/emitted depends on upper and lower levels
Higher energy levels are close together
Above a certain energy, electron can escape     (ionization)
Series of lines named for bottom level
To get absorption, lower level must be occupied
Depends upon temperature of atoms
To get emission, upper level must be occupied
Can get down-ward cascade through many levels